The Derivation of the Berglund Estimator for the Diffusion Constant

Introduction

I spent a lot of time working on modeling the movement of repair enzymes in DNA. For various reasons, publication of the results was delayed, but I wanted to share this derivation of the Berglund estimator of the diffusion constant (Berglund 2010) and (Michalet and Berglund 2012) as it took me so long to work out!.

Berglund, A. J. 2010. “Statistics of Camera-Based Single-Particle Tracking.” Journal Article. Phys Rev E Stat Nonlin Soft Matter Phys 82 (1 Pt 1): 011917. https://doi.org/10.1103/PhysRevE.82.011917.

Michalet, Xavier, and Andrew J. Berglund. 2012. “Optimal Diffusion Coefficient Estimation in Single-Particle Tracking.” Phys. Rev. E 85 (June): 061916. https://doi.org/10.1103/PhysRevE.85.061916.

PDF with the derivation