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Related Experiment Video

Updated: Jan 15, 2026

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
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Super-Resolved Anomalous Diffusion: Deciphering the Joint Distribution of Anomalous Exponent and Diffusion

Yann Lanoiselée1, Gianni Pagnini1,2, Agnieszka Wyłomańska3

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|October 12, 2025
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Summary

This study addresses variability in anomalous diffusion (α and D) observed in experiments. We developed methods to distinguish true parameter populations from finite-duration recording effects, offering guidelines for data fitting.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Anomalous diffusion describes molecular motion in heterogeneous media using mean-squared displacement.
  • Experimental studies report populations of anomalous diffusion parameters (α and D), leading to observed variability.
  • Distinguishing true parameter populations from finite-duration recording artifacts is crucial for accurate interpretation.

Purpose of the Study:

  • To disentangle the contributions of parameter populations and finite-duration recordings to anomalous diffusion variability.
  • To introduce and analyze novel estimators for anomalous diffusion parameters.
  • To provide a theoretical framework and practical guidelines for analyzing experimental data.

Main Methods:

  • Development of estimators based on time-averaged mean-squared displacement.
  • Application of a copula approach to derive the joint density function of parameter estimations.
  • Comparison with numerical simulations of fractional Brownian motion.
  • Quantification of accuracy using Hellinger distance.

Main Results:

  • A universal methodology applicable to Gaussian processes and quadratic time-averaged statistics was introduced.
  • A formula for the joint density function of estimated anomalous diffusion parameters was derived.
  • The experimentally observed relation D∝exp(αc_{1}+c_{2}) was theoretically explained with an exact expression.
  • Numerical simulations validated the theoretical findings and accuracy.

Conclusions:

  • The developed methodology effectively distinguishes between true parameter populations and finite-duration recording effects in anomalous diffusion.
  • The study provides a theoretical basis for understanding the relationship between anomalous diffusion parameters.
  • Practical guidelines and routines are offered for fitting experimental data, enhancing the analysis of molecular motion in complex systems.