The Laws of Sensitivity for Small Nonequilibrium Systems

Explore the laws of sensitivity for small systems in this Santa Fe Institute lecture. Delve into the challenge of understanding chemical mechanisms responsible for molecular sensitivity in living organisms. Discover how constraints on sensitivity relate to system structure and fluctuations at equilibrium, and learn about newly uncovered laws constraining sensitivity in small, nonequilibrium systems. Examine the extension and unification of prior biophysics results on biochemical switches, sensors, and molecular discrimination. Investigate a nonequilibrium binding mechanism with remarkable sensitivity and its implications for gene regulation models. Gain insights into topics such as hemoglobin binding, chemotaxis in E. coli, and the flagellar motor. Understand the Markov chain tree theorem and its role in analyzing nonequilibrium steady states. Explore various types of perturbations and their effects on system sensitivity, including nested hysteresis and driving forces in edge perturbations.

Laws of sensitivity for small systems
At equilibrium, physics provides powerful tools to relate sensitivity (response to a perturbation) to system Structure
Binding to hemoglobin
Hill's explanation • Binding curve shape can be explained by multiple oxygen hemoglobin (Hil 1910)
A simple equilibrium law
Alienagerie of nonequilibrium sensitivity mechanisms...
Chemotaxis in E. coli
Quantifying sensitivity
Counting bound CheY-P...
Two sides of an equation
Kinetic schemes
Equilibrium vs. nonequilibrium
A common picture
Back to the flagellar motor
Tu's motor model
Key tool underlying results • There is an exact, algebraic expression for the nonequilibrium steady state probabilities in terms of transition rates. (Markov chain tree theorem)
Types of perturbations . Parameterize the transition rates like this
Tiuctuations determine sensitivity to vertex perturbations
Revisiting the flagellar motor
Nested hysteresis
Where to next?
Driving forces bound sensitivity to (symmetric) edge perturbations
Unifying the menagerie