# Duncan Lecture Series AMS Seminar: Stuart Geman (Brown University) @ Shaffer 100

**Title: **Random Walks on Secondary Structure and the Folding of RNA

**Abstract:**

What is the correct characterization of the native structure of a protein or a non-coding RNA molecule? Is it the minimum energy state, a metastable state, or a sample from thermal equilibrium? The problem is unsettled and a topic of enduring debate. The “agnostic” approach is through molecular dynamics—make a proper accounting of the intramolecular forces and interactions with the surrounding liquid (mostly water), write down the corresponding kinetic equation (e.g. a Langevin equation), and simulate folding. But this usually isn’t practical, and approximations need to be made. I will explore an approximation in which the bulk of the folding process is replaced by a random walk, with discrete moves from one secondary structure to another. An analytic result identifies conditions for guaranteed accuracy. Simulation results, running the approximation against an optimized integrator of the Langevin equation, achieve the expected accuracy, but 100 times faster.