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

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

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**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

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

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

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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-<br/>Measurements of Single-Particle Trajectories Single-particle tracking techniques <br/>allow quantitative measurements of diusion<br/>at the single-molecule level. Recorded time-series are mostly short and<br/>contain considerable measurement noise. The standard method for estimating<br/>diusion coecients from single-particle trajectories is based on leastsquares<br/>tting to the experimentally measured mean square displacements.<br/>This method is highly inecient, since it ignores the high correlations inherent<br/>in these. We derive the exact maximum likelihood estimator for the diusion<br/>coecient, valid for short time-series, along with an exact benchmark for the<br/>maximum precision attainable with any unbiased estimator, the Cramer-Rao<br/>bound. We propose a simple analytical and unbiased covariance-based estimator<br/>based on the autocovariance function and derive an exact analytical<br/>expression of its moment generating function. We nd that the maximum<br/>likelihood estimator exceeds the precision set by the Cramer-Rao bound, but<br/>at the cost of a small bias, while the covariance-based estimator, which is born<br/>unbiased, is almost optimal for all experimentally relevant parameter values.<br/>We extend the methods to particles diusing on a <br/>uctuating substrate, e.g., exible or semi exible polymers such as DNA, and show that <br/>uctuations induce an important bias in the estimates of diusion coecients if they are not<br/>accounted for. We apply the methods to obtain precise estimates of diusion<br/>coecients of hOgg1 repair proteins diusing on stretched uctuating DNA<br/>from data previously analyzed using a suboptimal method. Our analysis shows<br/>that the proteins have dierent eective diusion coecients and that their<br/>diusion coecients are correlated with their residence time on DNA. These<br/>results imply a multi-state model for hOgg1's diusion on DNA.

AB - Optimal Estimation of Diusion Coecients from Noisy Time-Lapse-<br/>Measurements of Single-Particle Trajectories Single-particle tracking techniques <br/>allow quantitative measurements of diusion<br/>at the single-molecule level. Recorded time-series are mostly short and<br/>contain considerable measurement noise. The standard method for estimating<br/>diusion coecients from single-particle trajectories is based on leastsquares<br/>tting to the experimentally measured mean square displacements.<br/>This method is highly inecient, since it ignores the high correlations inherent<br/>in these. We derive the exact maximum likelihood estimator for the diusion<br/>coecient, valid for short time-series, along with an exact benchmark for the<br/>maximum precision attainable with any unbiased estimator, the Cramer-Rao<br/>bound. We propose a simple analytical and unbiased covariance-based estimator<br/>based on the autocovariance function and derive an exact analytical<br/>expression of its moment generating function. We nd that the maximum<br/>likelihood estimator exceeds the precision set by the Cramer-Rao bound, but<br/>at the cost of a small bias, while the covariance-based estimator, which is born<br/>unbiased, is almost optimal for all experimentally relevant parameter values.<br/>We extend the methods to particles diusing on a <br/>uctuating substrate, e.g., exible or semi exible polymers such as DNA, and show that <br/>uctuations induce an important bias in the estimates of diusion coecients if they are not<br/>accounted for. We apply the methods to obtain precise estimates of diusion<br/>coecients of hOgg1 repair proteins diusing on stretched uctuating DNA<br/>from data previously analyzed using a suboptimal method. Our analysis shows<br/>that the proteins have dierent eective diusion coecients and that their<br/>diusion coecients are correlated with their residence time on DNA. These<br/>results 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 -