Understanding Patterns in the Living World

Introduction

• The living world is full of shapes and patterns.
• The mystery: how does variety arise from simple ingredients like cells and chemical instructions?
• There is a mathematical code that can describe these biological patterns, known as Turing patterns.

The Case of the Zebra

• Question: What color is a zebra? Answer: Black with white stripes.
• Common misconception: stripes are for camouflage against predators.
• Actual purpose: to confuse biting flies.
• This leads to deeper questions about the origin of such patterns.

Alan Turing and Morphogenesis

• Alan Turing (1952):
  • Published a paper proposing simple mathematical rules that explain various natural patterns.
  • Often known as a wartime codebreaker and father of modern computing.
• Turing's interest in biology stemmed from its complexity and the unknown factors that mathematics can help describe.
• Morphogenesis: The process of how living things grow and form shapes.

Reaction-Diffusion Model

• Turing's paper, The Chemical Basis of Morphogenesis, introduced equations that describe how patterns arise from simple initial conditions.
• Morphogens: Two chemicals that spread and react with each other at different rates.
• Key concepts:
  • Diffusion: Spreading of chemicals (like gas in a box).
  • Reaction: How chemicals interact as they spread.
• Turing combined diffusion and reaction to explain how patterns form, countering the belief that diffusion stabilizes systems.

Mechanism of Pattern Formation

• Turing's model involves:
  • An Activator: stimulates itself and produces an Inhibitor.
  • The inhibitor suppresses the activator.
• Example: Cheetah's spots can be understood using this model:
  • Fire (activator) creates spots as firefighters (inhibitor) control the spread.
• By altering variables in Turing's equations, different patterns (spots, stripes) can emerge.

Historical Context and Rediscovery

• Turing's ideas were initially ignored, overshadowed by discoveries like the structure of DNA.
• In the 1970s, scientists Gierer and Meinhardt rediscovered Turing patterns, leading to further interest in biological patterns.
• Biologists sought to find actual morphogens that matched Turing's predictions.

Real-World Applications of Turing's Theory

• Recent discoveries: molecules that create patterns in developing organisms.
• Examples include:
  • Mouse mouth ridges
  • Bird feather spacing
  • Shark denticle scales
• More complex systems, like mammal limb development, involve multiple signals and interactions.

Legacy of Alan Turing

• Turing faced personal struggles and societal challenges due to his sexuality, leading to a tragic end.
• His contributions were only recognized posthumously, with a pardon in 2013.
• Turing's work is significant in both biology and computing, inspiring modern inquiries into the mathematics of nature.
• Impact: Turing's findings showcase the intersection between math and biology, emphasizing mathematics' role in understanding the natural world.

Conclusion

• Turing's work illustrates that mathematics is not only a tool for description but also a key to understanding the complexities of life.
• Encouragement to remain curious and explore the connections between disciplines.