## Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories

Publication: Research › Ph.D. thesis – Annual report year: 2012

### Standard

**Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories.** / Vestergaard, Christian Lyngby; Flyvbjerg, Henrik (Supervisor).

Publication: Research › Ph.D. thesis – Annual report year: 2012

### Harvard

*Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories*. Ph.D. thesis.

### APA

*Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories*.

### CBE

### MLA

### Vancouver

### Author

### Bibtex

}

### RIS

TY - BOOK

T1 - Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories

AU - Vestergaard,Christian Lyngby

A2 - Flyvbjerg,Henrik

PY - 2012

Y1 - 2012

N2 - Optimal Estimation of Diusion Coecients from Noisy Time-Lapse-Measurements of Single-Particle Trajectories Single-particle tracking techniques allow quantitative measurements of diusionat the single-molecule level. Recorded time-series are mostly short andcontain considerable measurement noise. The standard method for estimatingdiusion coecients from single-particle trajectories is based on leastsquarestting to the experimentally measured mean square displacements.This method is highly inecient, since it ignores the high correlations inherentin these. We derive the exact maximum likelihood estimator for the diusioncoecient, valid for short time-series, along with an exact benchmark for themaximum precision attainable with any unbiased estimator, the Cramer-Raobound. We propose a simple analytical and unbiased covariance-based estimatorbased on the autocovariance function and derive an exact analyticalexpression of its moment generating function. We nd that the maximumlikelihood estimator exceeds the precision set by the Cramer-Rao bound, butat the cost of a small bias, while the covariance-based estimator, which is bornunbiased, is almost optimal for all experimentally relevant parameter values.We extend the methods to particles diusing on a uctuating substrate, e.g., exible or semi exible polymers such as DNA, and show that uctuations induce an important bias in the estimates of diusion coecients if they are notaccounted for. We apply the methods to obtain precise estimates of diusioncoecients of hOgg1 repair proteins diusing on stretched uctuating DNAfrom data previously analyzed using a suboptimal method. Our analysis showsthat the proteins have dierent eective diusion coecients and that theirdiusion coecients are correlated with their residence time on DNA. Theseresults imply a multi-state model for hOgg1's diusion on DNA.

AB - Optimal Estimation of Diusion Coecients from Noisy Time-Lapse-Measurements of Single-Particle Trajectories Single-particle tracking techniques allow quantitative measurements of diusionat the single-molecule level. Recorded time-series are mostly short andcontain considerable measurement noise. The standard method for estimatingdiusion coecients from single-particle trajectories is based on leastsquarestting to the experimentally measured mean square displacements.This method is highly inecient, since it ignores the high correlations inherentin these. We derive the exact maximum likelihood estimator for the diusioncoecient, valid for short time-series, along with an exact benchmark for themaximum precision attainable with any unbiased estimator, the Cramer-Raobound. We propose a simple analytical and unbiased covariance-based estimatorbased on the autocovariance function and derive an exact analyticalexpression of its moment generating function. We nd that the maximumlikelihood estimator exceeds the precision set by the Cramer-Rao bound, butat the cost of a small bias, while the covariance-based estimator, which is bornunbiased, is almost optimal for all experimentally relevant parameter values.We extend the methods to particles diusing on a uctuating substrate, e.g., exible or semi exible polymers such as DNA, and show that uctuations induce an important bias in the estimates of diusion coecients if they are notaccounted for. We apply the methods to obtain precise estimates of diusioncoecients of hOgg1 repair proteins diusing on stretched uctuating DNAfrom data previously analyzed using a suboptimal method. Our analysis showsthat the proteins have dierent eective diusion coecients and that theirdiusion coecients are correlated with their residence time on DNA. Theseresults imply a multi-state model for hOgg1's diusion on DNA.

M3 - Ph.D. thesis

BT - Optimal Estimation of Diffusion Coefficients from Noisy Time-Lapse-Recorded Single-Particle Trajectories

ER -