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Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach

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  • Muszkieta, Monika
  • Janczura, Joanna
  • Weron, Aleksander

Abstract

An ongoing rapid development in single particle tracking techniques has opened new possibilities for analysis of particles dynamics inside living cells. Assuming that the motion is governed by a fractional Brownian motion, we have generated a synthetic video resembling a real one from an experimental video of G-proteins and coupled with them receptors inside living cells. Next, we applied Brownian bridge method to study two fundamental analysis tasks on trajectory data: segmentation and classification in context of experimental data. We have shown that, depending on the method of dealing with missing data, the obtained results might vary significantly, obviously influencing the final conclusions.

Suggested Citation

  • Muszkieta, Monika & Janczura, Joanna & Weron, Aleksander, 2021. "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308559
    DOI: 10.1016/j.amc.2020.125902
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    References listed on IDEAS

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    1. Titiwat Sungkaworn & Marie-Lise Jobin & Krzysztof Burnecki & Aleksander Weron & Martin J. Lohse & Davide Calebiro, 2017. "Single-molecule imaging reveals receptor–G protein interactions at cell surface hot spots," Nature, Nature, vol. 550(7677), pages 543-547, October.
    2. Martin Lysy & Natesh S. Pillai & David B. Hill & M. Gregory Forest & John W. R. Mellnik & Paula A. Vasquez & Scott A. McKinley, 2016. "Model Comparison and Assessment for Single Particle Tracking in Biological Fluids," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1413-1426, October.
    3. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
    4. Kehr, K.W. & Kutner, R., 1982. "Random walk on a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(3), pages 535-549.
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    1. Janczura, Joanna & Burnecki, Krzysztof & Muszkieta, Monika & Stanislavsky, Aleksander & Weron, Aleksander, 2022. "Classification of random trajectories based on the fractional Lévy stable motion," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. 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).

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