8.592 - HST.452J (Fall 2024)

Statistical Physics in Biology

Lecture 25

1. 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 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)

(Lecture Notes)

Chromatin Organization (part II)

1. Determinants of nucleosome position
   • Sequence dependent positioning 
     • AAATTT... repels nucleosomes, possibly due to rigidity
     • Nucleosome attracting sequences; typically composed of AA, TT, AT and more flexible(and possibly bent) in one direction
   • Statistical positioning
     • Erlang distribution for probability of k non-overlapping nucleosomes in an interval
2. Genome packing
   • Wrapping aroud nucleosomes of persistent DNA provides a compression factor of roughly 5
   • Chromatin fibre packed into nucleus (size 7-25\mu m)
   • Persistence length of the chromatin fibre should be of the order of 3-5 nuclesomes (each around 10nm in size) for 30-50nm
   • Treated as a random walk, a chromosome of 10^9 would occupy a size of around 30\mu m, possible in large oocytes
   • Expectations for the size of a polymer segment of size s in the random walk, and when confined to a size D
   • However, measurements of R(s)~s^{1/3} appear to indicate a different behavior for chromatin
   • Chromosome Conformation Capture (Job Dekker) provides a measure of connectivity
   • Hi Glass (viewer of Hi-C data)
   • The hard problem is to infer 3d structure from Hi-C data, can instead look at statistical properties
   • The fractal globule model seems to fit some statistical aspects of  the data

• 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