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Optimal Estimation of Diusion Coecients from Noisy Time-Lapse-
Measurements of Single-Particle Trajectories Single-particle tracking techniques
allow quantitative measurements of diusion
at the single-molecule level. Recorded time-series are mostly short and
contain considerable measurement noise. The standard method for estimating
diusion coecients from single-particle trajectories is based on leastsquares
tting to the experimentally measured mean square displacements.
This method is highly inecient, since it ignores the high correlations inherent
in these. We derive the exact maximum likelihood estimator for the diusion
coecient, valid for short time-series, along with an exact benchmark for the
maximum precision attainable with any unbiased estimator, the Cramer-Rao
bound. We propose a simple analytical and unbiased covariance-based estimator
based on the autocovariance function and derive an exact analytical
expression of its moment generating function. We nd that the maximum
likelihood estimator exceeds the precision set by the Cramer-Rao bound, but
at the cost of a small bias, while the covariance-based estimator, which is born
unbiased, 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 not
accounted for. We apply the methods to obtain precise estimates of diusion
coecients of hOgg1 repair proteins diusing on stretched uctuating DNA
from data previously analyzed using a suboptimal method. Our analysis shows
that the proteins have dierent eective diusion coecients and that their
diusion coecients are correlated with their residence time on DNA. These
results imply a multi-state model for hOgg1's diusion on DNA.
Original languageEnglish
Number of pages133
StatePublished - 2012
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ID: 9905550