Title: From Noise to Precision: Structural Buffering and the Law of Large Numbers as Principles for Robust Homeostasis and Rhythms
Abstract: Biological systems must maintain reliable functions — stable steady states or precise oscillations — despite pervasive molecular noise and perturbations. How do cells achieve such robustness? In this talk, I will discuss two complementary mathematical principles. For robust perfect adaptation, I will show how structural buffering in biochemical networks can make steady states robust to perturbations, and how feedback controllers can regulate not only the mean response but also cell-to-cell variability. For the mammalian circadian clock, I will show how the law of large numbers enables robust rhythms: indirect transcriptional repression targets thousands of activator molecules, while cooperative phosphorylation synchronizes molecular timing, converting noisy molecular events into precise oscillations. Together, these examples suggest that robustness in biology is not achieved by eliminating noise, but by organizing it — through network structure in homeostasis and through large-number averaging in oscillations.
Tiffany Leighton
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