8.592 - HST.452J (Spring 2013)

Statistical Physics in Biology

Lecture 23

1. Dynamics on networks:
   • Node variables evolving according to inputs from connected nodes
   • Examples- Chemical flux balance analysis (FBA), Neural networks
   • Possible collective outcomes: fixed points, temporal oscillations, spatial patterns, ...
2. Time indedpendent steady-states:
   • One dimensional systems, fixed points, Langevin noise
   • Gradient descent in higher dimensional systems
   • Hopfiel's model of neurons with graded response, PNAS 81, 3088 (1984).
   • An applet for demonstrating Associative Memory in the Hopfield Model
3. Stability of Fixed Points:
   • Linear stability matrix; eigenvectors and eigenvalues
   • Loss of stability from a real eigenvalue; stability exchange, bifurcation
   • Biological switches
   • Loss of stability from imaginary eigenvalues; Poincaré–Bendixson theorem and periodic orbits
   • Simple (harmonic) oscillator, and complex representation
4. Biochemical clocks:
   • The Belousov-Zhabotinsky Reaction (Video) (Explanation)
   • The cogs of a biological clock
   • Animations of biological clocks
   • The Repressilator [Elowitz and Liebler, Nature 403, 305 (2000)]
5. Synchronization:
   • Examples: heart pacemaker cells, fireflies, cicada
   • The Kuramoto model: (Math Insight Applet) (Cactus Applet) (Applet by Albert Diaz-Guilera)
   • Collective synchronization

(Lecture Notes)

• Computation in the brain
• Minicourse on computational neuroscience for physicists [8.515 by Prof. Sebastian Seung]
• Neural Networks [9.641 by Prof. Sebastian Seung]

Biological Clocks

• Internet Resources on Chronobiology, Biological Clocks and Rhythms
• Biotiming Tutorial
• Clockwork Genes (2000 Holiday lectures)
• The Belousov-Zhabotinsky Reaction applet
• BZ reaction video from Experiments on the web
• The Repressilator figures
• Firefly (flash synchrony)