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

Christian Lyngby Vestergaard

    Research output: Book/ReportPh.D. thesis

    1037 Downloads (Pure)

    Abstract

    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
    Place of PublicationKgs. Lyngby
    PublisherTechnical University of Denmark
    Number of pages133
    Publication statusPublished - 2012

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