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Summary

We developed a new method to accurately estimate the diffusion constant (D) in biological single-particle tracking. This approach accounts for motion blur, intermittent trajectories, and localization uncertainty for more reliable results.

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Area of Science:

  • Physics
  • Biophysics
  • Computational Biology

Background:

  • Brownian motion is fundamental to particle dynamics.
  • Estimating the diffusion constant (D) is crucial for single-particle tracking (SPT) in biology.
  • Accurate D estimation provides insights into particle environment and state via hydrodynamic radius.

Purpose of the Study:

  • To present a novel method for estimating the diffusion constant (D).
  • To incorporate practical experimental effects like motion blur, intermittent trajectories, and time-dependent localization uncertainty into D estimation.
  • To improve the accuracy and reliability of D estimation in biological SPT.

Main Methods:

  • Developed a maximum-likelihood estimation procedure.
  • Formulated a likelihood expression for discretely observed Brownian trajectories including experimental effects.
  • Employed three distinct methods for solving the likelihood expression.
  • Calculated and analyzed Fisher information to understand bounds on D estimation.

Main Results:

  • The new method accurately estimates D by accounting for motion blur, intermittent trajectories, and variable localization errors.
  • Localization uncertainties were shown to impose a lower bound on D estimation.
  • Information-based confidence intervals were established for the estimator.
  • Simulated data demonstrated the benefit of incorporating variable localization errors.

Conclusions:

  • The presented method offers a more robust estimation of the diffusion constant (D) in biological SPT.
  • Accounting for combined experimental artifacts is essential for precise D measurements.
  • The approach provides reliable confidence intervals, enhancing the interpretation of SPT data.