8.592 - HST.452J (Spring 2022)
Statistical Physics in Biology
Lecture 27
(Please note that lecture is being recorded)
8.592 in 4-265 on 04/27/2022 at 2:30PM
Bifurcations, clocks and synchronization
Stability of Fixed Points:
Linear stability matrix; eigenvectors and eigenvalues
Loss of stability from a real eigenvalue;
stability exchange, bifurcation
Biological applications of bifurcation theory
Biological switches
(
Genetic toggle switch
by
James Collins
)
Loss of stability from imaginary eigenvalues;
Poincaré–Bendixson theorem
and periodic orbits
Simple (harmonic) oscillator, and complex representation
Biochemical clocks:
The Belousov-Zhabotinsky Reaction
(
video
,
video
) (
Explanation
)
The cogs of a biological clock
Animations of biological clocks
(
offline
}
The Repressilator
[
Elowitz and Liebler, Nature
403
, 305 (2000)
]
Synchronization:
Examples:
firefly
,
fireflies
,
heart pacemaker cells
,
cicada
Phase synchronization model from Nlogo
Collective synchronization
The Kuramoto model: (
Math Insight Applet
) (
with more details
)
(
Lecture Notes
)
Some related links
Biological Clocks
Internet Resources on Chronobiology, Biological Clocks and Rhythms
Biotiming Tutorial
Clockwork Genes
(2000 Holiday lectures)
The Belousov-Zhabotinsky Reaction applet
The Repressilator figures
Firefly (flash synchrony)
8.592
lecture- last update 4/25/22 by M. Kardar