8.592 - HST.452J (Spring 2026)

Statistical Physics in Biology

Lecture 16

Protein-DNA kinetics

1. How to find the optimal site on DNA? What is the search (first passage) time, or binding rate?
   • Smoluchowsky computation of binding rate: Consider flux into sphere of radius r_0, fixed concentration c at infinity => k_s=4\pi D r_0
   • In water diffusion coefficient of TF is of order 30(um)^2/s; precise binding requires r_0 of order of a DNA bp=1/3 nm
   • Art Riggs measured this rate in water experimentally, and found answer 10^3 times larger than the Smoluchowsky rate.
   • Facilitated "diffusion"? Delbruck considered dimensional reduction on a membrane, followed by works by Berg and von Hippel (1d-3d search).

(Mirny Lecture note from 4/2022)

(Kardar notes)