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Optimal estimation of diffusion coefficients from single-particle trajectories.

Christian L Vestergaard1, Paul C Blainey2, Henrik Flyvbjerg1

  • 1Department of Micro- and Nanotechnology, Technical University of Denmark, Kongens Lyngby DK-2800, Denmark.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
PubMed
Summary

We developed a superior, unbiased covariance-based estimator (CVE) for determining particle diffusion coefficients from trajectory data. This method outperforms traditional mean squared displacement and maximum likelihood estimators, especially on fluctuating substrates.

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Area of Science:

  • Physics
  • Biophysics
  • Physical Chemistry

Background:

  • Accurate determination of diffusion coefficients is crucial for understanding particle dynamics in various systems.
  • Traditional methods like mean squared displacement (MSD) and maximum likelihood estimation (MLE) have limitations in accuracy and computational demand.
  • Diffusion on complex, fluctuating substrates presents unique challenges for accurate measurement.

Purpose of the Study:

  • To introduce and validate a novel, optimal, and unbiased covariance-based estimator (CVE) for diffusion coefficient determination.
  • To compare the performance of CVE against established methods like MSD and MLE, particularly in challenging experimental conditions.
  • To address and correct for biases introduced by substrate motion in diffusion measurements.

Main Methods:

  • Development of a regression-free, covariance-based estimator (CVE).
  • Comparison of CVE with MSD and maximum likelihood estimation (MLE) in various parameter ranges.
  • Extension of MLE to decouple particle diffusion from substrate motion on fluctuating substrates.
  • Application of estimators to human 8-oxoguanine DNA glycolase proteins diffusing on DNA.

Main Results:

  • The CVE is shown to be unbiased, regression-free, and superior to MSD-based methods.
  • In relevant experimental ranges, CVE outperforms even the computationally intensive MLE.
  • On fluctuating substrates, substrate motion introduces bias in CVE, necessitating an extended MLE for correction.
  • The corrected CVE provides optimal estimates even for short time series on fluctuating substrates.

Conclusions:

  • The covariance-based estimator (CVE) offers a highly accurate and efficient method for determining diffusion coefficients.
  • Accounting for substrate fluctuations is essential for precise diffusion measurements, as demonstrated with DNA glycolase proteins on DNA.
  • The developed methods provide robust tools for analyzing particle diffusion in complex biological and physical systems.