title: Optimal estimation of diffusion coefficients from single-particle trajectories.
abstract: How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.
authors.affiliation: Department of Micro- and Nanotechnology, Technical University of Denmark, Kongens Lyngby DK-2800, Denmark.
authors.forename: Christian L
authors.initials: CL
authors.lastname: Vestergaard
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Paul C
authors.initials: PC
authors.lastname: Blainey
authors.affiliation: Department of Micro- and Nanotechnology, Technical University of Denmark, Kongens Lyngby DK-2800, Denmark.
authors.forename: Henrik
authors.initials: H
authors.lastname: Flyvbjerg
mesh_terms: D000465:Algorithms; D001704:Biopolymers / Q000032:analysis / Q000737:chemistry*; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry*; D045647:DNA Glycosylases / Q000737:chemistry*; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical
chemical_list: D001704:Biopolymers; D004247:DNA; D045647:DNA Glycosylases; C483741:OGG1 protein, rat