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Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments

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  • Eldad Kepten
  • Aleksander Weron
  • Grzegorz Sikora
  • Krzysztof Burnecki
  • Yuval Garini

Abstract

Single particle tracking is an essential tool in the study of complex systems and biophysics and it is commonly analyzed by the time-averaged mean square displacement (MSD) of the diffusive trajectories. However, past work has shown that MSDs are susceptible to significant errors and biases, preventing the comparison and assessment of experimental studies. Here, we attempt to extract practical guidelines for the estimation of anomalous time averaged MSDs through the simulation of multiple scenarios with fractional Brownian motion as a representative of a large class of fractional ergodic processes. We extract the precision and accuracy of the fitted MSD for various anomalous exponents and measurement errors with respect to measurement length and maximum time lags. Based on the calculated precision maps, we present guidelines to improve accuracy in single particle studies. Importantly, we find that in some experimental conditions, the time averaged MSD should not be used as an estimator.

Suggested Citation

  • Eldad Kepten & Aleksander Weron & Grzegorz Sikora & Krzysztof Burnecki & Yuval Garini, 2015. "Guidelines for the Fitting of Anomalous Diffusion Mean Square Displacement Graphs from Single Particle Tracking Experiments," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-10, February.
    • Handle: RePEc:plo:pone00:0117722
    DOI: 10.1371/journal.pone.0117722
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    1. Gorka Muñoz-Gil & Giovanni Volpe & Miguel Angel Garcia-March & Erez Aghion & Aykut Argun & Chang Beom Hong & Tom Bland & Stefano Bo & J. Alberto Conejero & Nicolás Firbas & Òscar Garibo i Orts & Aless, 2021. "Objective comparison of methods to decode anomalous diffusion," Nature Communications, Nature, vol. 12(1), pages 1-16, December.
    2. Daniel Ramírez Montero & Humberto Sánchez & Edo Veen & Theo Laar & Belén Solano & John F. X. Diffley & Nynke H. Dekker, 2023. "Nucleotide binding halts diffusion of the eukaryotic replicative helicase during activation," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    3. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    4. Szarek, Dawid & Maraj-Zygmąt, Katarzyna & Sikora, Grzegorz & Krapf, Diego & Wyłomańska, Agnieszka, 2022. "Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Chapin S. Korosec & Ivan N. Unksov & Pradheebha Surendiran & Roman Lyttleton & Paul M. G. Curmi & Christopher N. Angstmann & Ralf Eichhorn & Heiner Linke & Nancy R. Forde, 2024. "Motility of an autonomous protein-based artificial motor that operates via a burnt-bridge principle," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    6. Muszkieta, Monika & Janczura, Joanna, 2023. "A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    7. Sikora, Grzegorz & Wyłomańska, Agnieszka & Krapf, Diego, 2018. "Recurrence statistics for anomalous diffusion regime change detection," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 380-394.

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