8.592 - HST.452J (Spring 2022)

Statistical Physics in Biology

Lecture 28

1. Biochemical clocks:
   • Loss of stability from imaginary eigenvalues; Poincaré–Bendixson theorem and periodic orbits
   • The Belousov-Zhabotinsky Reaction (video, video) (Explanation)
   • The cogs of a biological clock
   • Animations of biological clocks (offline)
2. Synchronization:
   • Examples: firefly, fireflies, heart pacemaker cells, cicada
   • Phase synchronization model from Nlogo
   • Collective synchronization
   • The Kuramoto model: (Math Insight Applet) (with more details)
3. Biological Patterns:
   • Morphogenesis is the process whereby a living organism develops form and structure, e.g.
   • Animal Coats and Pigmentation Patterns
   • 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)
     • Patterns may form in reaction/diffusion equations:
       • Long-range inhibition and short-range excitation
       • Well-defined size
       • Stripes or spots
       • Applet demonstrating   One dimensional linear stability
       • Demonstrations of two dimensional patterns: 

       

       (from web-page of H. Meinhardt 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)

(Lecture Notes)

• Spatial patterns in biology (Sitabhra Sinha)
• Visual Models of Morphogenesis
• Reaction Diffusion Equations and Animal Coat Patterns
• Theoretical aspects of pattern formation and neuronal development (MPI Tübingen)
• Primary pattern formation, organizing regions and regeneration (MPI Tübingen)
• The Alan Turing Internet Scrapbook Growth, Form and Crisis