8.592 - HST.452J (Fall 2025)

Statistical Physics in Biology

Lecture 23

1. Biological Patterns:
   • Morphogenesis is the process whereby a living organism develops form and structure, e.g.
   • Animal Coats and Patterns   (examples)
   • Where do spots come from? Turing's answer: morphogens
     • "The chemical basis of morphogenesis," A.M. Turing, Phil. Trans. Roy. Soc. 237, 37 (1952) (offline)     Wikipedia
     • Patterns may form in reaction/diffusion equations:
       • Long-range inhibition and short-range excitation
       • Well-defined size
       • Stripes or spots
       • Brusselator pattern formation-   One dimensional linear stability
       • Demonstrations of two dimensional patterns: 

       

       (from HansMeinhardt at MPU Tuebingen)

   • Biological Relevance?
     • "The impact of Turing's work on pattern formation in biology," P.K. Maini, Math. Today 40, 140 (2004) (offline)
   • Noise can increase range of (incoherent) Turing pattern formation.
     • "Fluctuation-driven Turing patterns," T. Butler and N. Goldenfeld, Phys. Rev. E 84, 011112 (2011).(offline)
2. Oscillating patterns:
   • The Belousov-Zhabotinsky Reaction (video, video)
   • Fakhri group spatiotemporal protein patterns (Nature Physics 2021) video

(Lecture Notes)

• Spatial patterns in biology (Sitabhra Sinha)
• Visual Models of Morphogenesis
• Reaction Diffusion Equations and Animal Coat Patterns
• The Alan Turing Internet Scrapbook Growth, Form and Crisis