#### Henrik Flyvbjerg, Danish Technical U, Optimal estimation of diffusion coefficients from noisy single-particle trajectories

Einstein argued in 1905 that the mean squared displacement of a microscopic particle suspended in a fluid at rest is proportional to time with the constant of proportionality giving the particle's diffusion coefficient. Since then, diffusion coefficients have been determined from particle trajectories by fitting a straight line to the observed mean squared displacement. This procedure is accurate, but not precise in any of its incarnations, yet dominates practice.

We present a simpler, optimal, and unbiased estimator of diffusion coefficients of freely diffusing particles in homogeneous media. It takes time-lapse recorded single-particle trajectories as input, is vastly superior to estimates based on the mean squared displacement as function of time, and is superior to Maximum Likelihood estimation for short trajectories. We extend this estimator to taught fluctuating substrates in a manner that removes the false contribution from substrate motion to the measured diffusion coefficient.

As a pertinent practical illustration of its power, this estimator reveals a two-state kinetics in the diffusion of hOGG1 protein on flow-stretched DNA, a fluctuating substrate. This kinetics is found in data that previously were analyzed with the mean squared displacement, which revealed only simple diffusion.

**Location:**
Joseph Henry Room, Jadwin Hall

**Date/Time: **03/11/13
at
12:00 pm
- 03/11/13
at
1:00 pm

**Category: **Biophysics

**Department: **Lewis-Sigler Institute